CN103292771A - Method for calculating part conicity based on minimum zone - Google Patents

Method for calculating part conicity based on minimum zone Download PDF

Info

Publication number
CN103292771A
CN103292771A CN2013102554642A CN201310255464A CN103292771A CN 103292771 A CN103292771 A CN 103292771A CN 2013102554642 A CN2013102554642 A CN 2013102554642A CN 201310255464 A CN201310255464 A CN 201310255464A CN 103292771 A CN103292771 A CN 103292771A
Authority
CN
China
Prior art keywords
contact point
value contact
point
low value
cone
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN2013102554642A
Other languages
Chinese (zh)
Other versions
CN103292771B (en
Inventor
陈磊磊
钟艳茹
孙永厚
黄美发
匡兵
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guilin University of Electronic Technology
Original Assignee
陈磊磊
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 陈磊磊 filed Critical 陈磊磊
Priority to CN201310255464.2A priority Critical patent/CN103292771B/en
Publication of CN103292771A publication Critical patent/CN103292771A/en
Application granted granted Critical
Publication of CN103292771B publication Critical patent/CN103292771B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Abstract

A method for calculating part conicity based on a minimum zone comprises the steps of firstly measuring and obtaining coordinates of measured points on the measured circular conical surface, then providing initial parameters of a cone, inquiring measured points of measured features in contact with an error tolerance zone, performing corresponding translation change, rotation change and size change of the error tolerance zone according to the number and coordinates of contact points, and calculating the change amount of the tolerance zone to sequentially find contact points meeting criterions of the minimum zone. By means of the method, a conicity error optimal value and a cone parameter optimal value can be accurately calculated.

Description

A kind of computing method of the part conicity based on Minimum Area
Technical field
The present invention relates to a kind of computing method of the part conicity based on Minimum Area, belong to delicate metering and computer application field, the qualification that can be used under the various situations circular cone key element in how much products detects, and provides guidance for the improvement of process and processing technology.
Background technology
The circular cone cooperation is widely used in the geometry of machinery product owing to have advantages such as good to neutrality, that sealing strong, it is reliable to cooperate, installation is fast and accurate for positioning.In actual production, generally adopt conventional metered dose utensils such as angular instrument, plug cone gage to carry out approval test.Though these methods are simple, detection information is too single, can not satisfy the requirement of high-accuracy mechanical product, has certain limitation.Along with the widespread use of high-accuracy digitized measurement equipment, more and more higher requirement is proposed taperness error evaluation algorithm.The assessment method of taperness error mainly contains Minimum Area method, imperial palace connection, minimum method for externally, least square method, has only the Minimum Area method to meet the tolerance definition, and result of calculation is minimum and unique, is the referee method that how much product errors are passed judgment on.
The Minimum Area method belongs to the non-differentiability complex optimization problem, and at present, Chinese scholars mainly adopts traditional optimization, intelligent algorithm, computational geometry method etc.Computational stability is poor, counting yield is low, number of spots is restricted to adopting, result of calculation is difficult to reach defectives such as exact solution owing to existing for these methods, causes the Minimum Area method to be difficult in the actual detected and uses.Generally all adopt ripe least square method to calculate the part taperness error approx in the market.
The evaluation of Minimum Area conicity is divided into two kinds, and a kind of is that cone angle is variable, and a kind of cone angle is theoretical value, is constant.
Summary of the invention
In order to overcome above-mentioned technical disadvantages, the purpose of this invention is to provide a kind of computing method of the part conicity based on Minimum Area.This method has not only improved the precision of surveying instrument detection taperness error, and algorithm stability is good, counting yield is high.
The computing method of a kind of part conicity based on Minimum Area of the present invention when cone angle is variable, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 2013102554642100002DEST_PATH_IMAGE002
, wherein =1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points Form the measuring point collection
Figure 2013102554642100002DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 2013102554642100002DEST_PATH_IMAGE010
, the circular cone axis direction vector
Figure 2013102554642100002DEST_PATH_IMAGE012
And semi-cone angle
Figure 2013102554642100002DEST_PATH_IMAGE014
Wherein
Figure 2013102554642100002DEST_PATH_IMAGE016
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Figure 2013102554642100002DEST_PATH_IMAGE018
Step 2: use following formula, calculate each measuring point successively
Figure 2013102554642100002DEST_PATH_IMAGE020
Distance to circular conical surface
Figure 2013102554642100002DEST_PATH_IMAGE022
,
Figure 2013102554642100002DEST_PATH_IMAGE024
Wherein
Figure 2013102554642100002DEST_PATH_IMAGE026
, all measuring point correspondences
Figure 238140DEST_PATH_IMAGE022
Form set
Figure 2013102554642100002DEST_PATH_IMAGE028
Record respectively ,
Figure 2013102554642100002DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 811073DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 2013102554642100002DEST_PATH_IMAGE034
, institute's record
Figure 590810DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region And according to ,
Figure 925025DEST_PATH_IMAGE032
With , calculate
Figure 2013102554642100002DEST_PATH_IMAGE038
Coordinate and the interior vertex of a cone that contains circular cone
Figure 2013102554642100002DEST_PATH_IMAGE040
Coordinate; This moment taperness error
Figure 2013102554642100002DEST_PATH_IMAGE042
=
Figure 2013102554642100002DEST_PATH_IMAGE044
Step 3: judge that whether the quantity of low value contact point in the set of low value contact point is less than 2;
If the quantity of low value contact point, is pressed the computing method of maximum inscribed circle awl less than 2, inquire about preceding 2 low value contact points, and calculate the parameter of circular cone, jump to step 2;
If the quantity of low value contact point is carried out next step more than or equal to 2.
Step 4: whether the quantity of judging low value contact point in the set of low value contact point equals 2;
If low value contact point quantity equals 2, then 2 low value contact points are effective contact point;
If low value contact point quantity greater than 2, then connects high value contact point and the outer vertex of a cone that contains circular cone respectively
Figure 806897DEST_PATH_IMAGE038
, connect the vertex of a cone of low value contact point and interior containing circular cone respectively
Figure 538092DEST_PATH_IMAGE040
, calculate successively 2 groups of straight lines with arbitrarily perpendicular to The intersection point on plane, can judgement find 2 low value contact points, the intersection point that connects 2 low value contact point correspondences obtains straight line l, the intersection point intersection point corresponding with all the other low value contact points that satisfies high value contact point correspondence is distributed in straight line respectively lBoth sides, if can not find 2 low value contact points that satisfy condition, then jump to step 6; If can find 2 low value contact points that satisfy condition, 2 low value contact points that then satisfy condition are effective contact point, jump to step 5.
Step 5: the intersection point that connects 2 effective low value contact point correspondences obtains straight line l 1, and in the corresponding intersection point set of high value contact, inquiry is apart from straight line l 1Nearest intersection point, then the high value contact point of this intersection point correspondence is effectively high value contact point; 2 effective low value contact points respectively with the vertex of a cone of interior containing circular cone
Figure 879261DEST_PATH_IMAGE040
Link to each other, 2 lines constitute 1 angle, calculate the equidistant point of this angle, and the normal vector of this equidistant point is the direction vector of containment region rotation change
Figure 2013102554642100002DEST_PATH_IMAGE046
If
Figure 2013102554642100002DEST_PATH_IMAGE048
Be 1 effective low value contact point wherein,
Figure 2013102554642100002DEST_PATH_IMAGE050
Be effectively high value contact point;
With 1 noncontact measuring point wherein
Figure 2013102554642100002DEST_PATH_IMAGE052
Be calculating object, calculate
Figure 2013102554642100002DEST_PATH_IMAGE054
Equidistant point, and calculate this equidistant point and mistake
Figure 2013102554642100002DEST_PATH_IMAGE056
And normal vector is
Figure 209748DEST_PATH_IMAGE046
The intersection on plane
Figure 2013102554642100002DEST_PATH_IMAGE058
, calculate then
Figure 795450DEST_PATH_IMAGE014
Deduct
Figure 225294DEST_PATH_IMAGE058
With
Figure 2013102554642100002DEST_PATH_IMAGE060
Angle, obtain
Figure 2013102554642100002DEST_PATH_IMAGE062
Travel through all noncontact measuring points, the calculating correspondence
Figure 591554DEST_PATH_IMAGE062
, all measuring point correspondences
Figure 928994DEST_PATH_IMAGE062
Form set
Figure 2013102554642100002DEST_PATH_IMAGE064
, in set
Figure 165940DEST_PATH_IMAGE064
Middle element of rejecting less than 0;
Again with a noncontact measuring point Be calculating object, do
Figure 2013102554642100002DEST_PATH_IMAGE066
Equidistant point, and calculate this equidistant point and mistake And normal vector is
Figure 354662DEST_PATH_IMAGE046
The intersection on plane
Figure 2013102554642100002DEST_PATH_IMAGE070
, calculate then
Figure 433477DEST_PATH_IMAGE014
Deduct With
Figure 2013102554642100002DEST_PATH_IMAGE072
Angle, obtain
Figure 2013102554642100002DEST_PATH_IMAGE074
Travel through all noncontact measuring points, the calculating correspondence
Figure 839454DEST_PATH_IMAGE074
, all measuring point correspondences
Figure 258934DEST_PATH_IMAGE074
Form set
Figure 2013102554642100002DEST_PATH_IMAGE076
, in set
Figure 203756DEST_PATH_IMAGE076
Middle element of rejecting less than 0;
Query set , In minimum value, minimum value is the rotation variation of containment region On the direction that cone angle reduces, containment region around Rotation
Figure 481973DEST_PATH_IMAGE078
After, the parameter of calculating containment region
Figure 548018DEST_PATH_IMAGE038
,
Figure 661468DEST_PATH_IMAGE016
, ,
Figure 873323DEST_PATH_IMAGE068
, jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure 2013102554642100002DEST_PATH_IMAGE080
Direction vector
Figure 2013102554642100002DEST_PATH_IMAGE082
With zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure 2013102554642100002DEST_PATH_IMAGE084
,
Figure 2013102554642100002DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes
Figure 2013102554642100002DEST_PATH_IMAGE088
, zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Figure 2013102554642100002DEST_PATH_IMAGE092
Or
Figure 2013102554642100002DEST_PATH_IMAGE094
The rotation variation of containment region is set
Figure 246405DEST_PATH_IMAGE078
Initial value.
Step 7: calculate
Figure 530756DEST_PATH_IMAGE016
Around
Figure 2013102554642100002DEST_PATH_IMAGE096
Or Rotation
Figure 5599DEST_PATH_IMAGE078
Vector after the angle
Figure 2013102554642100002DEST_PATH_IMAGE100
With
Figure 2013102554642100002DEST_PATH_IMAGE102
,
Figure 2013102554642100002DEST_PATH_IMAGE104
Be the vertex of a cone, with
Figure 502440DEST_PATH_IMAGE100
For the axis direction vector, with
Figure 277498DEST_PATH_IMAGE014
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
Figure 2013102554642100002DEST_PATH_IMAGE106
,
Figure 2013102554642100002DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
Figure 936012DEST_PATH_IMAGE102
,
Figure 2013102554642100002DEST_PATH_IMAGE110
,
Figure 2013102554642100002DEST_PATH_IMAGE112
,
Figure 429310DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis
Figure 2013102554642100002DEST_PATH_IMAGE114
On, obtain respectively
Figure 2013102554642100002DEST_PATH_IMAGE116
,
Figure 2013102554642100002DEST_PATH_IMAGE118
,
Figure 2013102554642100002DEST_PATH_IMAGE120
,
Figure 2013102554642100002DEST_PATH_IMAGE122
, will cut and hand over circular projection on the plane
Figure 464262DEST_PATH_IMAGE114
On; Can set up the binary nonlinear system of equations by following relation,
Figure 2013102554642100002DEST_PATH_IMAGE124
Wherein ,
Figure 2013102554642100002DEST_PATH_IMAGE128
Be respectively
Figure 2013102554642100002DEST_PATH_IMAGE130
,
Figure 2013102554642100002DEST_PATH_IMAGE132
Corresponding cross section radius of circle,
Figure 2013102554642100002DEST_PATH_IMAGE134
After change
Figure 2013102554642100002DEST_PATH_IMAGE136
On the plane Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 188822DEST_PATH_IMAGE134
Coordinate; According to
Figure 169416DEST_PATH_IMAGE134
, ,
Figure 429813DEST_PATH_IMAGE128
,
Figure 226868DEST_PATH_IMAGE014
With
Figure 835704DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
Figure 2013102554642100002DEST_PATH_IMAGE138
,
Figure 2013102554642100002DEST_PATH_IMAGE140
According to the method for step 2, calculate the low value contact point contains circular cone outside containment region distance
Figure 2013102554642100002DEST_PATH_IMAGE142
, calculate high value contact point contains circular cone outside containment region distance
Figure 2013102554642100002DEST_PATH_IMAGE144
And then according to the method for step 2, calculate all noncontact measuring points contain circular cone outside containment region distance successively
Figure 71513DEST_PATH_IMAGE028
If And , then represent the variation deficiency, the anglec of rotation
Figure 82195DEST_PATH_IMAGE078
Become
Figure 2013102554642100002DEST_PATH_IMAGE150
If
Figure 2013102554642100002DEST_PATH_IMAGE152
Or
Figure 2013102554642100002DEST_PATH_IMAGE154
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Figure 518992DEST_PATH_IMAGE078
Become
Figure 2013102554642100002DEST_PATH_IMAGE156
Judge
Figure 208599DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 920203DEST_PATH_IMAGE018
If
Figure 785391DEST_PATH_IMAGE078
The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 924249DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 976518DEST_PATH_IMAGE100
,
Figure 226234DEST_PATH_IMAGE138
,
Figure 211507DEST_PATH_IMAGE140
Assignment is given respectively
Figure 521266DEST_PATH_IMAGE016
,
Figure 185466DEST_PATH_IMAGE056
,
Figure 2013102554642100002DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Figure 2013102554642100002DEST_PATH_IMAGE160
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is ,
Figure 2013102554642100002DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure 2013102554642100002DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
Figure 2013102554642100002DEST_PATH_IMAGE168
More than in two formulas ,
Figure 2013102554642100002DEST_PATH_IMAGE172
Figure 2013102554642100002DEST_PATH_IMAGE176
,
Figure 2013102554642100002DEST_PATH_IMAGE178
Figure 2013102554642100002DEST_PATH_IMAGE180
With
Figure 2013102554642100002DEST_PATH_IMAGE182
,
Figure 2013102554642100002DEST_PATH_IMAGE184
,
Figure 2013102554642100002DEST_PATH_IMAGE186
,
Figure 2013102554642100002DEST_PATH_IMAGE188
,
Figure 2013102554642100002DEST_PATH_IMAGE190
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 2013102554642100002DEST_PATH_IMAGE192
Assignment is given
Figure 363506DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure 2013102554642100002DEST_PATH_IMAGE194
Assignment is given
Figure 203286DEST_PATH_IMAGE160
Judge
Figure 683946DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 445229DEST_PATH_IMAGE018
If The difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 996613DEST_PATH_IMAGE018
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge whether high value contact equals 6 with low value contact point quantity sum;
If high value contact is not equal to 6 with low value contact point quantity sum; Jump to step 12; Otherwise carry out dimensional variations, set the dimensional variations amount
Figure 648174DEST_PATH_IMAGE160
Initial value.
Step 11: the method in the applying step 9, with ,
Figure 682175DEST_PATH_IMAGE184
,
Figure 230968DEST_PATH_IMAGE186
,
Figure 319010DEST_PATH_IMAGE188
, ,
Figure 253785DEST_PATH_IMAGE014
Be unknown quantity, set up Nonlinear System of Equations, error of calculation containment region width is
Figure 2013102554642100002DEST_PATH_IMAGE196
The time the containment region parameter;
The method of applying step 7 has judged whether that according to change back containment region parameter measuring point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 657084DEST_PATH_IMAGE192
Assignment is given If there is not measuring point to exceed containment region, then will
Figure 263832DEST_PATH_IMAGE194
Assignment is given
Judge
Figure 524229DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 954073DEST_PATH_IMAGE018
If less than, illustrate and find the 7th contact point, jump to step 12; Otherwise, carry out dimensional variations again, the operation of repeating step 11.
Step 12: judge that whether high value contact and low value contact point quantity sum are more than or equal to 7;
If high value contact and low value contact point contact point quantity sum are more than or equal to 7, with in the contact point set 6 be 1 combination, be calculating object with 6 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 10,11 is adjusted
Figure 398961DEST_PATH_IMAGE160
Size; If
Figure 939664DEST_PATH_IMAGE160
Less than the error permissible value of setting , judge whether to satisfy criterion, jump to step 13 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
Figure 918301DEST_PATH_IMAGE160
, judge that again iteration is gone down successively; If
Figure 647223DEST_PATH_IMAGE160
Greater than the error permissible value of setting
Figure 319513DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 7.
Step 13: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Another kind of the present invention is based on the computing method of the part conicity of Minimum Area, and when cone angle was constant, the calculation process when being variable with cone angle was similar substantially, and difference is to keep cone angle constant in the containment region change, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 817490DEST_PATH_IMAGE002
, wherein
Figure 323558DEST_PATH_IMAGE004
=1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Figure 539775DEST_PATH_IMAGE006
Form the measuring point collection
Figure 891122DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 243606DEST_PATH_IMAGE010
, the circular cone axis direction vector
Figure 186154DEST_PATH_IMAGE012
According to drawing information, obtain semi-cone angle
Figure 624089DEST_PATH_IMAGE014
Wherein
Figure 638181DEST_PATH_IMAGE016
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Figure 110751DEST_PATH_IMAGE018
Step 2: use following formula, calculate each measuring point successively
Figure 958621DEST_PATH_IMAGE020
Distance to circular conical surface
Figure 883852DEST_PATH_IMAGE022
,
Figure 577002DEST_PATH_IMAGE024
Wherein
Figure 904078DEST_PATH_IMAGE026
, all measuring point correspondences
Figure 188429DEST_PATH_IMAGE022
Form set
Figure 194431DEST_PATH_IMAGE028
Record respectively
Figure 425692DEST_PATH_IMAGE030
,
Figure 607274DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 656002DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 555825DEST_PATH_IMAGE034
, institute's record
Figure 121935DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region And according to
Figure 253019DEST_PATH_IMAGE016
,
Figure 640138DEST_PATH_IMAGE032
With
Figure 337836DEST_PATH_IMAGE030
, calculate
Figure 494011DEST_PATH_IMAGE038
Coordinate and the interior vertex of a cone that contains circular cone
Figure 291066DEST_PATH_IMAGE040
Coordinate; This moment taperness error
Figure 368743DEST_PATH_IMAGE042
=
Figure 542235DEST_PATH_IMAGE044
Figure 552917DEST_PATH_IMAGE030
Step 3: the quantity of judging low value contact point in the low value contact point set whether less than 2 or high value contact point set in the quantity of high value contact point whether less than 2;
If the quantity of the quantity of low value contact point and high value contact point jumps to step: 6 all greater than 2;
If the quantity of low value contact point less than 2 or the quantity of high value contact point less than 2, carry out coordinate transform, make
Figure 114348DEST_PATH_IMAGE016
With coordinate system zThe axle forward is in the same way parallel, each measuring point
Figure 2013102554642100002DEST_PATH_IMAGE198
Become after the change
Figure 2013102554642100002DEST_PATH_IMAGE200
, jump to next step.
Step 4: respectively with each measuring point be the summit, with
Figure 679322DEST_PATH_IMAGE014
For semi-cone angle, with
Figure 2013102554642100002DEST_PATH_IMAGE202
Be the axis direction vector, construct circumscribed auxiliary circular cone, do Auxiliary plane, calculate each circumscribed auxiliary circular cone and plane
Figure 718822DEST_PATH_IMAGE204
Common factor, its common factor is one and cut hands over circle, the cutting of all circumscribed auxiliary circular cone correspondences handed over circle to constitute to cut and handed over the circle set
Figure 849589DEST_PATH_IMAGE064
Respectively with each measuring point be the summit, with
Figure 457288DEST_PATH_IMAGE014
For semi-cone angle, with
Figure 40716DEST_PATH_IMAGE016
Be the axis direction vector, the auxiliary circular cone of structure inscribe; Do
Figure 2013102554642100002DEST_PATH_IMAGE206
Auxiliary plane, calculate the auxiliary circular cone of each inscribe and plane
Figure 290431DEST_PATH_IMAGE206
Common factor, its common factor is one and cut hands over circle, the cutting of the auxiliary circular cone correspondence of all inscribes handed over circle to constitute to cut and handed over the circle set
Figure 869180DEST_PATH_IMAGE076
Step 5: will gather respectively
Figure 178939DEST_PATH_IMAGE064
,
Figure 249663DEST_PATH_IMAGE076
In the circular projection of cut handing over be parallel to arbitrarily XoyOn the plane of coordinate plane, obtain cutting and hand over circle to gather
Figure 2013102554642100002DEST_PATH_IMAGE208
,
Figure 2013102554642100002DEST_PATH_IMAGE210
On projection plane, calculate 1 donut, satisfy interior circle and the set of donut
Figure 771911DEST_PATH_IMAGE208
In 2 cut to hand over circle circumscribed, the cylindrical of donut and set
Figure 611691DEST_PATH_IMAGE210
In 2 cut to hand over the circle inscribes, the line at two point of contacts that the line at two point of contacts that the interior circle of donut is corresponding is corresponding with the cylindrical of donut has and intersects; According to concentrically ringed central coordinate of circle,
Figure 697545DEST_PATH_IMAGE014
Calculate
Figure 989986DEST_PATH_IMAGE040
,
Figure 847084DEST_PATH_IMAGE038
Jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure 541371DEST_PATH_IMAGE080
Direction vector
Figure 661773DEST_PATH_IMAGE082
With zAfter axle is parallel, high value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure 707090DEST_PATH_IMAGE084
,
Figure 102299DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes ,
Figure 332609DEST_PATH_IMAGE090
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Figure 599642DEST_PATH_IMAGE092
Or
Figure 532963DEST_PATH_IMAGE094
The rotation variation of containment region is set
Figure 201842DEST_PATH_IMAGE078
Initial value.
Step 7: calculate
Figure 929627DEST_PATH_IMAGE016
Around
Figure 418377DEST_PATH_IMAGE096
Or
Figure 420968DEST_PATH_IMAGE098
Rotation
Figure 944353DEST_PATH_IMAGE078
Vector after the angle With
Figure 943719DEST_PATH_IMAGE102
,
Figure 484422DEST_PATH_IMAGE104
Be the vertex of a cone, with For the axis direction vector, with
Figure 931901DEST_PATH_IMAGE014
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
Figure 395243DEST_PATH_IMAGE106
,
Figure 739637DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
Figure 237614DEST_PATH_IMAGE102
,
Figure 743682DEST_PATH_IMAGE110
,
Figure 553375DEST_PATH_IMAGE112
,
Figure 435880DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis
Figure 788364DEST_PATH_IMAGE114
On, obtain respectively
Figure 465333DEST_PATH_IMAGE116
,
Figure 372109DEST_PATH_IMAGE118
,
Figure 58306DEST_PATH_IMAGE120
, , will cut and hand over circular projection on the plane
Figure 378745DEST_PATH_IMAGE114
On; Can set up the binary nonlinear system of equations by following relation,
Figure 897451DEST_PATH_IMAGE124
Wherein ,
Figure 448836DEST_PATH_IMAGE128
Be respectively ,
Figure 880134DEST_PATH_IMAGE132
Corresponding cross section radius of circle,
Figure 376974DEST_PATH_IMAGE134
After change
Figure 558557DEST_PATH_IMAGE136
On the plane
Figure 13809DEST_PATH_IMAGE114
Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 913632DEST_PATH_IMAGE134
Coordinate; According to
Figure 73218DEST_PATH_IMAGE134
,
Figure 109307DEST_PATH_IMAGE126
,
Figure 735460DEST_PATH_IMAGE128
, With
Figure 226802DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
Figure 851818DEST_PATH_IMAGE138
,
Figure 648873DEST_PATH_IMAGE140
According to the method for step 2, calculate the distance of low value contact point female surface outside containment region
Figure 257709DEST_PATH_IMAGE142
, calculate the high distance that is worth contact point female surface outside containment region
Figure 165622DEST_PATH_IMAGE144
And then according to the method for step 2, calculate the distance of all noncontact measuring points female surface outside containment region successively
Figure 769778DEST_PATH_IMAGE028
If
Figure 737734DEST_PATH_IMAGE146
And
Figure 833866DEST_PATH_IMAGE148
, then represent the variation deficiency, the anglec of rotation
Figure 545470DEST_PATH_IMAGE078
Become
Figure 145079DEST_PATH_IMAGE150
If
Figure 283936DEST_PATH_IMAGE152
Or
Figure 601785DEST_PATH_IMAGE154
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Figure 117080DEST_PATH_IMAGE078
Become
Figure 102354DEST_PATH_IMAGE156
Judge
Figure 5588DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 810733DEST_PATH_IMAGE018
If The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 703919DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 653421DEST_PATH_IMAGE100
, , Assignment is given respectively
Figure 762825DEST_PATH_IMAGE016
,
Figure 7862DEST_PATH_IMAGE056
,
Figure 787599DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
Figure 997180DEST_PATH_IMAGE162
,
Figure 819643DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure 555518DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
Figure 754418DEST_PATH_IMAGE168
More than in two formulas ,
Figure 416660DEST_PATH_IMAGE172
Figure 170990DEST_PATH_IMAGE174
Figure 767056DEST_PATH_IMAGE176
,
Figure 290441DEST_PATH_IMAGE178
Figure 454707DEST_PATH_IMAGE180
With
Figure 696332DEST_PATH_IMAGE182
,
Figure 705876DEST_PATH_IMAGE184
,
Figure 83768DEST_PATH_IMAGE186
,
Figure 684514DEST_PATH_IMAGE188
, Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will Assignment is given
Figure 318123DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure 89770DEST_PATH_IMAGE194
Assignment is given
Figure 509250DEST_PATH_IMAGE160
Judge
Figure 391756DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 744240DEST_PATH_IMAGE018
If
Figure 280263DEST_PATH_IMAGE160
The difference of the iterative value that front and back are twice is less than the error permissible value of setting , illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge that whether high value contact and low value contact point quantity sum are more than or equal to 6;
If high value contact and low value contact point contact point quantity sum are more than or equal to 6, with in the contact point set 5 be 1 combination, be calculating object with 5 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 8,9 is adjusted Size; If
Figure 611384DEST_PATH_IMAGE160
Less than the error permissible value of setting
Figure 724834DEST_PATH_IMAGE018
, judge whether to satisfy criterion, jump to step 11 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
Figure 118906DEST_PATH_IMAGE160
, judge that again iteration is gone down successively; If Greater than the error permissible value of setting
Figure 263766DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 6.
Step 11: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Beneficial effect of the present invention is: the contact point relative position that this method inquires satisfies the Minimum Area criterion, and parameter and the taperness error of the actual circular cone corresponding ideal circular cone that calculates are optimal value, and computational stability is good, counting yield is high.
To those skilled in the art, according to use design disclosed by the invention, can easily carry out various distortion and change to the present invention program, should be noted in the discussion above that all these distortion and change all should belong to scope of the present invention.
Description of drawings
Minimum Area conicity calculation flow chart when Fig. 1 is variable for cone angle of the present invention.
Embodiment
Embodiment 1:
A kind of computing method of the part conicity based on Minimum Area when cone angle is variable, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 282537DEST_PATH_IMAGE002
, wherein
Figure 695064DEST_PATH_IMAGE004
=1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Figure 723063DEST_PATH_IMAGE006
Form the measuring point collection
Figure 373487DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 828739DEST_PATH_IMAGE010
, the circular cone axis direction vector
Figure 462983DEST_PATH_IMAGE012
And semi-cone angle Wherein Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Figure 19232DEST_PATH_IMAGE018
Step 2: use following formula, calculate each measuring point successively Distance to circular conical surface ,
Figure 260223DEST_PATH_IMAGE024
Wherein
Figure 57278DEST_PATH_IMAGE026
, all measuring point correspondences
Figure 134955DEST_PATH_IMAGE022
Form set
Figure 42869DEST_PATH_IMAGE028
Record respectively
Figure 53550DEST_PATH_IMAGE030
,
Figure 614981DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 711113DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 422717DEST_PATH_IMAGE034
, institute's record
Figure 756747DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region
Figure 895604DEST_PATH_IMAGE036
And according to
Figure 479032DEST_PATH_IMAGE016
,
Figure 587802DEST_PATH_IMAGE032
With
Figure 307497DEST_PATH_IMAGE030
, calculate
Figure 617255DEST_PATH_IMAGE038
Coordinate and the interior vertex of a cone that contains circular cone
Figure 687980DEST_PATH_IMAGE040
Coordinate; This moment taperness error
Figure 741386DEST_PATH_IMAGE042
=
Figure 530668DEST_PATH_IMAGE030
Step 3: judge that whether the quantity of low value contact point in the set of low value contact point is less than 2;
If the quantity of low value contact point, is pressed the computing method of maximum inscribed circle awl less than 2, inquire about preceding 2 low value contact points, and calculate the parameter of circular cone, jump to step 2;
If the quantity of low value contact point is carried out next step more than or equal to 2.
Step 4: whether the quantity of judging low value contact point in effective low value contact point set equals 2;
If low value contact point quantity equals 2, then 2 low value contact points are effective contact point;
If low value contact point quantity greater than 2, then connects high value contact point and the outer vertex of a cone that contains circular cone respectively
Figure 88688DEST_PATH_IMAGE038
, connect the vertex of a cone of low value contact point and interior containing circular cone respectively
Figure 680206DEST_PATH_IMAGE040
, calculate successively 2 groups of straight lines with arbitrarily perpendicular to
Figure 967968DEST_PATH_IMAGE016
The intersection point on plane, can judgement find 2 low value contact points, the intersection point that connects 2 low value contact point correspondences obtains straight line l, the intersection point intersection point corresponding with all the other low value contact points that satisfies high value contact point correspondence is distributed in straight line respectively lBoth sides, if can not find 2 low value contact points that satisfy condition, then jump to step 6; If can find 2 low value contact points that satisfy condition, 2 low value contact points that then satisfy condition are effective contact point, jump to step 5.
Step 5: the intersection point that connects 2 low value contact point correspondences obtains straight line l 1, and in the corresponding intersection point set of high value contact, inquiry is apart from straight line l 1Nearest intersection point, then the high value contact point of this intersection point correspondence is effectively high value contact point; 2 effective low value contact points respectively with the vertex of a cone of interior containing circular cone
Figure 885109DEST_PATH_IMAGE040
Link to each other, 2 lines constitute 1 angle, calculate the equidistant point of this angle, and the normal vector of this equidistant point is the direction vector of containment region rotation change
Figure 664846DEST_PATH_IMAGE046
If
Figure 60055DEST_PATH_IMAGE048
Be 1 effective low value contact point wherein,
Figure 343269DEST_PATH_IMAGE050
Be effectively high value contact point;
With 1 noncontact measuring point wherein
Figure 165731DEST_PATH_IMAGE052
Be calculating object, calculate
Figure 432765DEST_PATH_IMAGE054
Equidistant point, and calculate this equidistant point and mistake And normal vector is
Figure 894019DEST_PATH_IMAGE046
The intersection on plane
Figure 887383DEST_PATH_IMAGE058
, calculate then
Figure 641712DEST_PATH_IMAGE014
Deduct With
Figure 370951DEST_PATH_IMAGE060
Angle, obtain
Figure 800795DEST_PATH_IMAGE062
Travel through all noncontact measuring points, the calculating correspondence
Figure 42420DEST_PATH_IMAGE062
, all measuring point correspondences
Figure 317544DEST_PATH_IMAGE062
Form set
Figure 961015DEST_PATH_IMAGE064
, in set
Figure 889657DEST_PATH_IMAGE064
Middle element of rejecting less than 0;
Again with a noncontact measuring point
Figure 618578DEST_PATH_IMAGE052
Be calculating object, do
Figure 697393DEST_PATH_IMAGE066
Equidistant point, and calculate this equidistant point and mistake
Figure 195370DEST_PATH_IMAGE068
And normal vector is
Figure 967017DEST_PATH_IMAGE046
The intersection on plane , calculate then
Figure 269002DEST_PATH_IMAGE014
Deduct
Figure 621486DEST_PATH_IMAGE070
With
Figure 564035DEST_PATH_IMAGE072
Angle, obtain
Figure 1969DEST_PATH_IMAGE074
Travel through all noncontact measuring points, the calculating correspondence
Figure 16062DEST_PATH_IMAGE074
, all measuring point correspondences
Figure 488631DEST_PATH_IMAGE074
Form set
Figure 602081DEST_PATH_IMAGE076
, in set
Figure 996153DEST_PATH_IMAGE076
Middle element of rejecting less than 0;
Query set
Figure 220461DEST_PATH_IMAGE064
, In minimum value, minimum value is the rotation variation of containment region
Figure 566309DEST_PATH_IMAGE078
On the direction that cone angle reduces, containment region around
Figure 978835DEST_PATH_IMAGE046
Rotation
Figure 600310DEST_PATH_IMAGE078
After, the parameter of calculating containment region
Figure 781892DEST_PATH_IMAGE038
,
Figure 971565DEST_PATH_IMAGE016
,
Figure 871388DEST_PATH_IMAGE014
,
Figure 906340DEST_PATH_IMAGE068
, jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure 208008DEST_PATH_IMAGE080
Direction vector With zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure 955702DEST_PATH_IMAGE084
,
Figure 918978DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes
Figure 809574DEST_PATH_IMAGE088
,
Figure 606629DEST_PATH_IMAGE090
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Figure 215465DEST_PATH_IMAGE092
Or
Figure 857799DEST_PATH_IMAGE094
The rotation variation of containment region is set
Figure 868480DEST_PATH_IMAGE078
Initial value.
Step 7: calculate
Figure 836436DEST_PATH_IMAGE016
Around Or
Figure 237647DEST_PATH_IMAGE098
Rotation
Figure 102835DEST_PATH_IMAGE078
Vector after the angle
Figure 241692DEST_PATH_IMAGE100
With
Figure 825121DEST_PATH_IMAGE102
,
Figure 74836DEST_PATH_IMAGE104
Be the vertex of a cone, with
Figure 528951DEST_PATH_IMAGE100
For the axis direction vector, with
Figure 838710DEST_PATH_IMAGE014
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
Figure 909434DEST_PATH_IMAGE106
,
Figure 962841DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will , ,
Figure 169197DEST_PATH_IMAGE112
,
Figure 26295DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis
Figure 720581DEST_PATH_IMAGE114
On, obtain respectively
Figure 840984DEST_PATH_IMAGE116
,
Figure 886300DEST_PATH_IMAGE118
, , , will cut and hand over circular projection on the plane
Figure 511820DEST_PATH_IMAGE114
On; Can set up the binary nonlinear system of equations by following relation,
Figure 778853DEST_PATH_IMAGE124
Wherein
Figure 977753DEST_PATH_IMAGE126
,
Figure 849894DEST_PATH_IMAGE128
Be respectively
Figure 702313DEST_PATH_IMAGE130
,
Figure 456642DEST_PATH_IMAGE132
Corresponding cross section radius of circle,
Figure 193654DEST_PATH_IMAGE134
After change
Figure 717039DEST_PATH_IMAGE136
On the plane
Figure 615725DEST_PATH_IMAGE114
Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 591771DEST_PATH_IMAGE134
Coordinate; According to
Figure 132474DEST_PATH_IMAGE134
,
Figure 369420DEST_PATH_IMAGE126
,
Figure 704587DEST_PATH_IMAGE128
,
Figure 902350DEST_PATH_IMAGE014
With
Figure 981164DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
Figure 72617DEST_PATH_IMAGE138
,
Figure 578685DEST_PATH_IMAGE140
According to the method for step 2, calculate the low value contact point contains circular cone outside containment region distance
Figure 794902DEST_PATH_IMAGE142
, calculate high value contact point contains circular cone outside containment region distance
Figure 677408DEST_PATH_IMAGE144
And then according to the method for step 2, calculate all noncontact measuring points contain circular cone outside containment region distance successively
Figure 498733DEST_PATH_IMAGE028
If
Figure 441281DEST_PATH_IMAGE146
And
Figure 879216DEST_PATH_IMAGE148
, then represent the variation deficiency, the anglec of rotation
Figure 893308DEST_PATH_IMAGE078
Become
Figure 834720DEST_PATH_IMAGE150
If Or , change excessively, there is measuring point to exceed containment region, the anglec of rotation
Figure 832129DEST_PATH_IMAGE078
Become
Figure 752680DEST_PATH_IMAGE156
Judge
Figure 37031DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 918399DEST_PATH_IMAGE018
If
Figure 680819DEST_PATH_IMAGE078
The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 862401DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 911129DEST_PATH_IMAGE100
,
Figure 810952DEST_PATH_IMAGE138
,
Figure 845904DEST_PATH_IMAGE140
Assignment is given respectively ,
Figure 508146DEST_PATH_IMAGE056
,
Figure 500459DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Figure 604682DEST_PATH_IMAGE160
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
Figure 229698DEST_PATH_IMAGE162
,
Figure 26753DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure 635589DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
Figure 809081DEST_PATH_IMAGE168
More than in two formulas
Figure 413238DEST_PATH_IMAGE170
,
Figure 850035DEST_PATH_IMAGE172
Figure 946167DEST_PATH_IMAGE174
Figure 392192DEST_PATH_IMAGE176
,
Figure 522959DEST_PATH_IMAGE178
Figure 255292DEST_PATH_IMAGE180
With
Figure 838720DEST_PATH_IMAGE182
, ,
Figure 73709DEST_PATH_IMAGE186
,
Figure 383468DEST_PATH_IMAGE188
,
Figure 923034DEST_PATH_IMAGE190
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 976440DEST_PATH_IMAGE192
Assignment is given
Figure 816220DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure 296880DEST_PATH_IMAGE194
Assignment is given
Judge
Figure 39894DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 734181DEST_PATH_IMAGE018
If
Figure 385742DEST_PATH_IMAGE160
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 431058DEST_PATH_IMAGE018
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge whether high value contact equals 6 with low value contact point quantity sum;
If high value contact is not equal to 6 with low value contact point quantity sum; Jump to step 12; Otherwise carry out dimensional variations, set the dimensional variations amount
Figure 295109DEST_PATH_IMAGE160
Initial value.
Step 11: the method in the applying step 9, with
Figure 843902DEST_PATH_IMAGE182
,
Figure 931944DEST_PATH_IMAGE184
,
Figure 198977DEST_PATH_IMAGE186
, ,
Figure 394652DEST_PATH_IMAGE190
,
Figure 653595DEST_PATH_IMAGE014
Be unknown quantity, set up Nonlinear System of Equations, error of calculation containment region width is The time the containment region parameter;
The method of applying step 7 has judged whether that according to change back containment region parameter measuring point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 144936DEST_PATH_IMAGE192
Assignment is given
Figure 137163DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure 301428DEST_PATH_IMAGE194
Assignment is given
Figure 543054DEST_PATH_IMAGE160
Judge Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 461648DEST_PATH_IMAGE018
If less than, illustrate and find the 7th contact point, jump to step 12; Otherwise, carry out dimensional variations again, the operation of repeating step 11.
Step 12: judge that whether high value contact and low value contact point quantity sum are more than or equal to 7;
If high value contact and low value contact point contact point quantity sum are more than or equal to 7, with in the contact point set 6 be 1 combination, be calculating object with 6 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 10,11 is adjusted
Figure 655869DEST_PATH_IMAGE160
Size; If
Figure 119211DEST_PATH_IMAGE160
Less than the error permissible value of setting
Figure 463605DEST_PATH_IMAGE018
, judge whether to satisfy criterion, jump to step 13 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
Figure 961583DEST_PATH_IMAGE160
, judge that again iteration is gone down successively; If
Figure 936492DEST_PATH_IMAGE160
Greater than the error permissible value of setting
Figure 152710DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 7.
Step 13: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
Embodiment 2:
A kind of computing method of the part conicity based on Minimum Area, similar substantially with the calculation process of embodiment 1 when cone angle is constant, difference is to keep cone angle constant in the containment region change, mainly may further comprise the steps:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 35215DEST_PATH_IMAGE002
, wherein
Figure 387699DEST_PATH_IMAGE004
=1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Figure 64668DEST_PATH_IMAGE006
Form the measuring point collection
Figure 96078DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 782274DEST_PATH_IMAGE010
, the circular cone axis direction vector According to drawing information, obtain semi-cone angle
Figure 102714DEST_PATH_IMAGE014
Wherein
Figure 27945DEST_PATH_IMAGE016
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Step 2: use following formula, calculate each measuring point successively
Figure 48170DEST_PATH_IMAGE020
Distance to circular conical surface
Figure 332521DEST_PATH_IMAGE022
,
Figure 479469DEST_PATH_IMAGE024
Wherein , all measuring point correspondences
Figure 282525DEST_PATH_IMAGE022
Form set
Figure 737778DEST_PATH_IMAGE028
Record respectively
Figure 637600DEST_PATH_IMAGE030
,
Figure 203711DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 708642DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 334795DEST_PATH_IMAGE034
, institute's record
Figure 456335DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region
Figure 826136DEST_PATH_IMAGE036
And according to ,
Figure 372841DEST_PATH_IMAGE032
With , calculate
Figure 889590DEST_PATH_IMAGE038
Coordinate and the interior vertex of a cone that contains circular cone
Figure 900272DEST_PATH_IMAGE040
Coordinate; This moment taperness error
Figure 337069DEST_PATH_IMAGE042
=
Figure 433201DEST_PATH_IMAGE044
Figure 144805DEST_PATH_IMAGE030
Step 3: the quantity of judging low value contact point in the low value contact point set whether less than 2 or high value contact point set in the quantity of high value contact point whether less than 2;
If the quantity of the quantity of low value contact point and high value contact point jumps to step: 6 all greater than 2;
If the quantity of low value contact point less than 2 or the quantity of high value contact point less than 2, carry out coordinate transform, make
Figure 275572DEST_PATH_IMAGE016
With coordinate system zThe axle forward is in the same way parallel, each measuring point
Figure 414430DEST_PATH_IMAGE198
Become after the change
Figure 325754DEST_PATH_IMAGE200
, jump to next step.
Step 4: respectively with each measuring point be the summit, with
Figure 841049DEST_PATH_IMAGE014
For semi-cone angle, with
Figure 826322DEST_PATH_IMAGE202
Be the axis direction vector, construct circumscribed auxiliary circular cone, do
Figure 136081DEST_PATH_IMAGE204
Auxiliary plane, calculate each circumscribed auxiliary circular cone and plane
Figure 410067DEST_PATH_IMAGE204
Common factor, its common factor is one and cut hands over circle, the cutting of all circumscribed auxiliary circular cone correspondences handed over circle to constitute to cut and handed over the circle set
Respectively with each measuring point be the summit, with
Figure 303254DEST_PATH_IMAGE014
For semi-cone angle, with
Figure 783914DEST_PATH_IMAGE016
Be the axis direction vector, the auxiliary circular cone of structure inscribe; Do
Figure 341934DEST_PATH_IMAGE206
Auxiliary plane, calculate the auxiliary circular cone of each inscribe and plane
Figure 526928DEST_PATH_IMAGE206
Common factor, its common factor is one and cut hands over circle, the cutting of the auxiliary circular cone correspondence of all inscribes handed over circle to constitute to cut and handed over the circle set
Figure 955635DEST_PATH_IMAGE076
Step 5: will gather respectively
Figure 607196DEST_PATH_IMAGE064
,
Figure 386934DEST_PATH_IMAGE076
In the circular projection of cut handing over be parallel to arbitrarily XoyOn the plane of coordinate plane, obtain cutting and hand over circle to gather
Figure 782143DEST_PATH_IMAGE208
,
Figure 189990DEST_PATH_IMAGE210
On projection plane, calculate 1 donut, satisfy interior circle and the set of donut
Figure 12453DEST_PATH_IMAGE208
In 2 cut to hand over circle circumscribed, the cylindrical of donut and set
Figure 279486DEST_PATH_IMAGE210
In 2 cut to hand over the circle inscribes, the line at two point of contacts that the line at two point of contacts that the interior circle of donut is corresponding is corresponding with the cylindrical of donut has and intersects; According to concentrically ringed central coordinate of circle,
Figure 947228DEST_PATH_IMAGE014
Calculate ,
Figure 609470DEST_PATH_IMAGE038
Jump to step 2.
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure 363800DEST_PATH_IMAGE080
Direction vector
Figure 959866DEST_PATH_IMAGE082
With zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure 483252DEST_PATH_IMAGE084
,
Figure 116358DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes ,
Figure 898686DEST_PATH_IMAGE090
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Figure 870053DEST_PATH_IMAGE092
Or
Figure 470799DEST_PATH_IMAGE094
The rotation variation of containment region is set
Figure 402983DEST_PATH_IMAGE078
Initial value.
Step 7: calculate
Figure 747377DEST_PATH_IMAGE016
Around
Figure 979775DEST_PATH_IMAGE096
Or
Figure 689DEST_PATH_IMAGE098
Rotation
Figure 951328DEST_PATH_IMAGE078
Vector after the angle
Figure 427309DEST_PATH_IMAGE100
With
Figure 29060DEST_PATH_IMAGE102
,
Figure 971608DEST_PATH_IMAGE104
Be the vertex of a cone, with
Figure 409543DEST_PATH_IMAGE100
For the axis direction vector, with
Figure 564581DEST_PATH_IMAGE014
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously ,
Figure 478496DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
Figure 403727DEST_PATH_IMAGE102
,
Figure 628035DEST_PATH_IMAGE110
,
Figure 423952DEST_PATH_IMAGE112
,
Figure 36199DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis On, obtain respectively
Figure 476725DEST_PATH_IMAGE116
, ,
Figure 113560DEST_PATH_IMAGE120
, , will cut and hand over circular projection on the plane
Figure 782755DEST_PATH_IMAGE114
On; Can set up the binary nonlinear system of equations by following relation,
Figure 84424DEST_PATH_IMAGE124
Wherein ,
Figure 425592DEST_PATH_IMAGE128
Be respectively
Figure 795394DEST_PATH_IMAGE130
, Corresponding cross section radius of circle,
Figure 748623DEST_PATH_IMAGE134
After change
Figure 357459DEST_PATH_IMAGE136
On the plane
Figure 734214DEST_PATH_IMAGE114
Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 744895DEST_PATH_IMAGE134
Coordinate; According to
Figure 712851DEST_PATH_IMAGE134
,
Figure 808983DEST_PATH_IMAGE126
, ,
Figure 979250DEST_PATH_IMAGE014
With
Figure 118108DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards ,
Figure 685672DEST_PATH_IMAGE140
According to the method for step 2, calculate the distance of low value contact point female surface outside containment region , calculate the high distance that is worth contact point female surface outside containment region
Figure 715125DEST_PATH_IMAGE144
And then according to the method for step 2, calculate the distance of all noncontact measuring points female surface outside containment region successively
Figure 785849DEST_PATH_IMAGE028
If
Figure 839256DEST_PATH_IMAGE146
And
Figure 272511DEST_PATH_IMAGE148
, then represent the variation deficiency, the anglec of rotation
Figure 753171DEST_PATH_IMAGE078
Become
Figure 311192DEST_PATH_IMAGE150
If
Figure 902710DEST_PATH_IMAGE152
Or , change excessively, there is measuring point to exceed containment region, the anglec of rotation Become
Figure 762716DEST_PATH_IMAGE156
Judge
Figure 157925DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting If
Figure 388235DEST_PATH_IMAGE078
The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 655268DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 854168DEST_PATH_IMAGE100
,
Figure 523047DEST_PATH_IMAGE138
,
Figure 985252DEST_PATH_IMAGE140
Assignment is given respectively
Figure 739582DEST_PATH_IMAGE016
,
Figure 476594DEST_PATH_IMAGE056
,
Figure 999979DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7.
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Figure 23299DEST_PATH_IMAGE160
Initial value.
Step 9: establish high value contact point coordinate, low value contact point coordinate is
Figure 264924DEST_PATH_IMAGE162
,
Figure 540048DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure 183519DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
Figure 987527DEST_PATH_IMAGE168
More than in two formulas
Figure 716448DEST_PATH_IMAGE170
,
Figure 795263DEST_PATH_IMAGE172
Figure 293240DEST_PATH_IMAGE174
Figure 658362DEST_PATH_IMAGE176
,
Figure 609001DEST_PATH_IMAGE178
Figure 491506DEST_PATH_IMAGE180
With
Figure 843990DEST_PATH_IMAGE182
,
Figure 786538DEST_PATH_IMAGE184
,
Figure 693314DEST_PATH_IMAGE186
,
Figure 113931DEST_PATH_IMAGE188
, Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 699951DEST_PATH_IMAGE192
Assignment is given
Figure 625181DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure 442965DEST_PATH_IMAGE194
Assignment is given
Figure 504461DEST_PATH_IMAGE160
Judge
Figure 788812DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 201339DEST_PATH_IMAGE018
If The difference of the iterative value that front and back are twice is less than the error permissible value of setting , illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9.
Step 10: judge that whether high value contact and low value contact point quantity sum are more than or equal to 6;
If high value contact and low value contact point contact point quantity sum are more than or equal to 6, with in the contact point set 5 be 1 combination, be calculating object with 5 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 8,9 is adjusted
Figure 69435DEST_PATH_IMAGE160
Size; If
Figure 969258DEST_PATH_IMAGE160
Less than the error permissible value of setting , judge whether to satisfy criterion, jump to step 11 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
Figure 837037DEST_PATH_IMAGE160
, judge that again iteration is gone down successively; If Greater than the error permissible value of setting
Figure 189924DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 6.
Step 11: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.

Claims (4)

1. computing method based on the part conicity of Minimum Area when the cone angle of circular cone is variable, is characterized in that concrete steps are as follows:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 2013102554642100001DEST_PATH_IMAGE002
, wherein
Figure 2013102554642100001DEST_PATH_IMAGE004
=1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Figure 2013102554642100001DEST_PATH_IMAGE006
Form the measuring point collection
Figure 2013102554642100001DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 2013102554642100001DEST_PATH_IMAGE010
, the circular cone axis direction vector
Figure 2013102554642100001DEST_PATH_IMAGE012
And semi-cone angle
Figure 2013102554642100001DEST_PATH_IMAGE014
Wherein
Figure 2013102554642100001DEST_PATH_IMAGE016
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Figure 2013102554642100001DEST_PATH_IMAGE018
Step 2: use following formula, calculate each measuring point successively Distance to circular conical surface
Figure 2013102554642100001DEST_PATH_IMAGE022
,
Figure 2013102554642100001DEST_PATH_IMAGE024
Wherein
Figure 2013102554642100001DEST_PATH_IMAGE026
, all measuring point correspondences Form set Record respectively
Figure 2013102554642100001DEST_PATH_IMAGE030
,
Figure 2013102554642100001DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 140140DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 2013102554642100001DEST_PATH_IMAGE034
, institute's record
Figure 542389DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region
Figure 2013102554642100001DEST_PATH_IMAGE036
According to
Figure 213542DEST_PATH_IMAGE016
,
Figure 980510DEST_PATH_IMAGE032
With
Figure 53508DEST_PATH_IMAGE030
, calculate Coordinate and the interior vertex of a cone that contains circular cone
Figure 2013102554642100001DEST_PATH_IMAGE040
Coordinate; This moment taperness error
Figure 2013102554642100001DEST_PATH_IMAGE042
=
Figure 2013102554642100001DEST_PATH_IMAGE044
Figure 146098DEST_PATH_IMAGE030
Step 3: judge that whether the quantity of low value contact point in the set of low value contact point is less than 2;
If the quantity of low value contact point, is pressed the computing method of maximum inscribed circle awl less than 2, inquire about preceding 2 low value contact points, and calculate the parameter of circular cone, jump to step 2;
If the quantity of low value contact point is carried out next step more than or equal to 2;
Step 4: whether the quantity of judging low value contact point in the set of low value contact point equals 2;
If low value contact point quantity equals 2, then 2 low value contact points are effective contact point;
If low value contact point quantity greater than 2, then connects high value contact point and the outer vertex of a cone that contains circular cone respectively
Figure 711071DEST_PATH_IMAGE038
, connect the vertex of a cone of low value contact point and interior containing circular cone respectively
Figure 422675DEST_PATH_IMAGE040
, calculate successively 2 groups of straight lines with arbitrarily perpendicular to
Figure 287863DEST_PATH_IMAGE016
The intersection point on plane, can judgement find 2 low value contact points, the intersection point that connects 2 low value contact point correspondences obtains straight line l, the intersection point intersection point corresponding with all the other low value contact points that satisfies high value contact point correspondence is distributed in straight line respectively lBoth sides, if can not find 2 low value contact points that satisfy condition, then jump to step 6; If can find 2 low value contact points that satisfy condition, 2 low value contact points that then satisfy condition are effective contact point, jump to step 5;
Step 5: the intersection point that connects 2 effective low value contact point correspondences obtains straight line l 1, and in the corresponding intersection point set of high value contact, inquiry is apart from straight line l 1Nearest intersection point, then the high value contact point of this intersection point correspondence is effectively high value contact point; 2 effective low value contact points respectively with the vertex of a cone of interior containing circular cone
Figure 20196DEST_PATH_IMAGE040
Link to each other, 2 lines constitute 1 angle, calculate the equidistant point of this angle, and the normal vector of this equidistant point is the direction vector of containment region rotation change If
Figure 2013102554642100001DEST_PATH_IMAGE048
Be 1 effective low value contact point wherein,
Figure 2013102554642100001DEST_PATH_IMAGE050
Be effectively high value contact point;
With 1 noncontact measuring point wherein
Figure 2013102554642100001DEST_PATH_IMAGE052
Be calculating object, calculate
Figure 2013102554642100001DEST_PATH_IMAGE054
Equidistant point, and calculate this equidistant point and mistake
Figure 2013102554642100001DEST_PATH_IMAGE056
And normal vector is
Figure 665941DEST_PATH_IMAGE046
The intersection on plane
Figure 2013102554642100001DEST_PATH_IMAGE058
, calculate then
Figure 915657DEST_PATH_IMAGE014
Deduct
Figure 900930DEST_PATH_IMAGE058
With
Figure 2013102554642100001DEST_PATH_IMAGE060
Angle, obtain
Figure 2013102554642100001DEST_PATH_IMAGE062
Travel through all noncontact measuring points, the calculating correspondence , all measuring point correspondences
Figure 750254DEST_PATH_IMAGE062
Form set
Figure 2013102554642100001DEST_PATH_IMAGE064
, in set
Figure 397136DEST_PATH_IMAGE064
Middle element of rejecting less than 0;
Again with a noncontact measuring point
Figure 236916DEST_PATH_IMAGE052
Be calculating object, do
Figure 2013102554642100001DEST_PATH_IMAGE066
Equidistant point, and calculate this equidistant point and mistake
Figure 2013102554642100001DEST_PATH_IMAGE068
And normal vector is
Figure 186418DEST_PATH_IMAGE046
The intersection on plane
Figure 2013102554642100001DEST_PATH_IMAGE070
, calculate then Deduct
Figure 929432DEST_PATH_IMAGE070
With
Figure 2013102554642100001DEST_PATH_IMAGE072
Angle, obtain
Figure 2013102554642100001DEST_PATH_IMAGE074
Travel through all noncontact measuring points, the calculating correspondence
Figure 92560DEST_PATH_IMAGE074
, all measuring point correspondences
Figure 744121DEST_PATH_IMAGE074
Form set , in set
Figure 851754DEST_PATH_IMAGE076
Middle element of rejecting less than 0;
Query set
Figure 246964DEST_PATH_IMAGE064
,
Figure 389232DEST_PATH_IMAGE076
In minimum value, minimum value is the rotation variation of containment region
Figure 2013102554642100001DEST_PATH_IMAGE078
On the direction that cone angle reduces, containment region around
Figure 477274DEST_PATH_IMAGE046
Rotation
Figure 744307DEST_PATH_IMAGE078
After, the parameter of calculating containment region
Figure 412049DEST_PATH_IMAGE038
,
Figure 815348DEST_PATH_IMAGE016
,
Figure 667767DEST_PATH_IMAGE014
,
Figure 422096DEST_PATH_IMAGE068
, jump to step 2;
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure DEST_PATH_IMAGE080
Direction vector
Figure DEST_PATH_IMAGE082
With zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure DEST_PATH_IMAGE084
,
Figure DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes
Figure DEST_PATH_IMAGE088
,
Figure DEST_PATH_IMAGE090
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is
Figure 2013102554642100001DEST_PATH_IMAGE092
Or The rotation variation of containment region is set Initial value;
Step 7: calculate Around
Figure 2013102554642100001DEST_PATH_IMAGE096
Or
Figure 2013102554642100001DEST_PATH_IMAGE098
Rotation
Figure 643496DEST_PATH_IMAGE078
Vector after the angle
Figure 2013102554642100001DEST_PATH_IMAGE100
With
Figure 2013102554642100001DEST_PATH_IMAGE102
,
Figure DEST_PATH_IMAGE104
Be the vertex of a cone, with
Figure 213018DEST_PATH_IMAGE100
For the axis direction vector, with
Figure 753720DEST_PATH_IMAGE014
Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously
Figure DEST_PATH_IMAGE106
,
Figure DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
Figure 866033DEST_PATH_IMAGE102
, , ,
Figure 201199DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis On, obtain respectively
Figure DEST_PATH_IMAGE116
,
Figure DEST_PATH_IMAGE118
,
Figure DEST_PATH_IMAGE120
,
Figure DEST_PATH_IMAGE122
, will cut and hand over circular projection on the plane
Figure 992438DEST_PATH_IMAGE114
On; Can set up the binary nonlinear system of equations by following relation,
Figure DEST_PATH_IMAGE124
Wherein
Figure DEST_PATH_IMAGE126
,
Figure DEST_PATH_IMAGE128
Be respectively
Figure DEST_PATH_IMAGE130
,
Figure DEST_PATH_IMAGE132
Corresponding cross section radius of circle,
Figure DEST_PATH_IMAGE134
After change
Figure DEST_PATH_IMAGE136
On the plane
Figure 664727DEST_PATH_IMAGE114
Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 631546DEST_PATH_IMAGE134
Coordinate; According to
Figure 137614DEST_PATH_IMAGE134
,
Figure 353832DEST_PATH_IMAGE126
, ,
Figure 588821DEST_PATH_IMAGE014
With
Figure 124845DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside containing circular cone of containment region afterwards ,
According to the method for step 2, calculate the low value contact point contains circular cone outside containment region distance
Figure DEST_PATH_IMAGE142
, calculate high value contact point contains circular cone outside containment region distance
Figure DEST_PATH_IMAGE144
And then according to the method for step 2, calculate all noncontact measuring points contain circular cone outside containment region distance successively If
Figure DEST_PATH_IMAGE146
And
Figure DEST_PATH_IMAGE148
, then represent the variation deficiency, the anglec of rotation
Figure 45713DEST_PATH_IMAGE078
Become
Figure DEST_PATH_IMAGE150
If
Figure DEST_PATH_IMAGE152
Or
Figure DEST_PATH_IMAGE154
, change excessively, there is measuring point to exceed containment region, the anglec of rotation Become
Figure DEST_PATH_IMAGE156
Judge
Figure 834995DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 353701DEST_PATH_IMAGE018
If
Figure 578009DEST_PATH_IMAGE078
The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 905085DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 189436DEST_PATH_IMAGE100
,
Figure 70804DEST_PATH_IMAGE138
,
Figure 833224DEST_PATH_IMAGE140
Assignment is given respectively
Figure 14806DEST_PATH_IMAGE016
, ,
Figure DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7;
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set Initial value;
Step 9: establish high value contact point coordinate, low value contact point coordinate is ,
Figure DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
More than in two formulas
Figure DEST_PATH_IMAGE170
,
Figure DEST_PATH_IMAGE172
Figure DEST_PATH_IMAGE176
,
Figure DEST_PATH_IMAGE178
Figure DEST_PATH_IMAGE180
With
Figure DEST_PATH_IMAGE182
,
Figure DEST_PATH_IMAGE184
,
Figure DEST_PATH_IMAGE186
, ,
Figure DEST_PATH_IMAGE190
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure DEST_PATH_IMAGE192
Assignment is given
Figure 150307DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will
Figure DEST_PATH_IMAGE194
Assignment is given
Figure 185259DEST_PATH_IMAGE160
Judge
Figure 221348DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 847502DEST_PATH_IMAGE018
If
Figure 828096DEST_PATH_IMAGE160
The difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 932318DEST_PATH_IMAGE018
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9;
Step 10: judge whether high value contact equals 6 with low value contact point quantity sum;
If high value contact is not equal to 6 with low value contact point quantity sum; Jump to step 12; Otherwise carry out dimensional variations, set the dimensional variations amount
Figure 88493DEST_PATH_IMAGE160
Initial value;
Step 11: the method in the applying step 9, with
Figure 885548DEST_PATH_IMAGE182
,
Figure 963225DEST_PATH_IMAGE184
, ,
Figure 147399DEST_PATH_IMAGE188
,
Figure 708830DEST_PATH_IMAGE190
, Be unknown quantity, set up Nonlinear System of Equations, error of calculation containment region width is
Figure DEST_PATH_IMAGE196
The time the containment region parameter;
The method of applying step 7 has judged whether that according to change back containment region parameter measuring point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 719829DEST_PATH_IMAGE192
Assignment is given If there is not measuring point to exceed containment region, then will
Figure 989453DEST_PATH_IMAGE194
Assignment is given
Figure 572881DEST_PATH_IMAGE160
Judge
Figure 416072DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 401346DEST_PATH_IMAGE018
If less than, illustrate and find the 7th contact point, jump to step 12; Otherwise, carry out dimensional variations again, the operation of repeating step 11;
Step 12: judge that whether high value contact and low value contact point quantity sum are more than or equal to 7;
If high value contact and low value contact point contact point quantity sum are more than or equal to 7, with in the contact point set 6 be 1 combination, be calculating object with 6 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 10,11 is adjusted
Figure 711105DEST_PATH_IMAGE160
Size; If
Figure 250670DEST_PATH_IMAGE160
Less than the error permissible value of setting
Figure 304077DEST_PATH_IMAGE018
, judge whether to satisfy criterion, jump to step 13 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate
Figure 143857DEST_PATH_IMAGE160
, judge that again iteration is gone down successively; If
Figure 624517DEST_PATH_IMAGE160
Greater than the error permissible value of setting
Figure 916958DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 7;
Step 13: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
3. computing method based on the part conicity of Minimum Area when the cone angle of circular cone is constant, is characterized in that concrete steps are as follows:
Step 1: tested circular cone is placed on the measuring table, in the measurement space rectangular coordinate system, measure and obtain the measuring point on the conical surface
Figure 367531DEST_PATH_IMAGE002
, wherein
Figure 61817DEST_PATH_IMAGE004
=1,2 ..., n, nRepresent the measuring point number and for greater than 7 positive integer; All measuring points
Figure 713379DEST_PATH_IMAGE006
Form the measuring point collection
Figure 758695DEST_PATH_IMAGE008
Provide the initial parameter of circular cone at random, comprise the outer vertex of a cone coordinate that contains circular cone
Figure 622746DEST_PATH_IMAGE010
, the circular cone axis direction vector According to drawing information, obtain semi-cone angle
Figure 259580DEST_PATH_IMAGE014
Wherein
Figure 526614DEST_PATH_IMAGE016
Direction vector is to point to big end by the circular cone small end; The specification error permissible value
Figure 53410DEST_PATH_IMAGE018
Step 2: use following formula, calculate each measuring point successively
Figure 722289DEST_PATH_IMAGE020
Distance to circular conical surface
Figure 981232DEST_PATH_IMAGE022
,
Figure 469982DEST_PATH_IMAGE024
Wherein
Figure 941415DEST_PATH_IMAGE026
, all measuring point correspondences Form set
Figure 629065DEST_PATH_IMAGE028
Record respectively ,
Figure 4869DEST_PATH_IMAGE032
Corresponding measuring point, institute's record
Figure 382760DEST_PATH_IMAGE030
Corresponding measuring point forms the low value contact point set of containment region
Figure 983506DEST_PATH_IMAGE034
, institute's record
Figure 446848DEST_PATH_IMAGE032
Corresponding measuring point forms the high value contact point set of containment region
Figure 260083DEST_PATH_IMAGE036
And according to
Figure 758061DEST_PATH_IMAGE016
,
Figure 264129DEST_PATH_IMAGE032
With , calculate
Figure 362852DEST_PATH_IMAGE038
Coordinate and the interior vertex of a cone that contains circular cone
Figure 308811DEST_PATH_IMAGE040
Coordinate; This moment taperness error =
Figure 423714DEST_PATH_IMAGE044
Figure 109911DEST_PATH_IMAGE030
Step 3: the quantity of judging low value contact point in the low value contact point set whether less than 2 or high value contact point set in the quantity of high value contact point whether less than 2;
If the quantity of the quantity of low value contact point and high value contact point jumps to step: 6 all greater than 2;
If the quantity of low value contact point less than 2 or the quantity of high value contact point less than 2, carry out coordinate transform, make With coordinate system zThe axle forward is in the same way parallel, each measuring point
Figure DEST_PATH_IMAGE198
Become after the change
Figure DEST_PATH_IMAGE200
, jump to next step;
Step 4: respectively with each measuring point be the summit, with
Figure 899192DEST_PATH_IMAGE014
For semi-cone angle, with
Figure DEST_PATH_IMAGE202
Be the axis direction vector, construct circumscribed auxiliary circular cone, do
Figure DEST_PATH_IMAGE204
Auxiliary plane, calculate each circumscribed auxiliary circular cone and plane Common factor, its common factor is one and cut hands over circle, the cutting of all circumscribed auxiliary circular cone correspondences handed over circle to constitute to cut and handed over the circle set
Figure 642206DEST_PATH_IMAGE064
Respectively with each measuring point be the summit, with
Figure 969282DEST_PATH_IMAGE014
For semi-cone angle, with
Figure 253633DEST_PATH_IMAGE016
Be the axis direction vector, the auxiliary circular cone of structure inscribe; Do
Figure DEST_PATH_IMAGE206
Auxiliary plane, calculate the auxiliary circular cone of each inscribe and plane
Figure 869422DEST_PATH_IMAGE206
Common factor, its common factor is one and cut hands over circle, the cutting of the auxiliary circular cone correspondence of all inscribes handed over circle to constitute to cut and handed over the circle set
Figure 897421DEST_PATH_IMAGE076
Step 5: will gather respectively
Figure 79004DEST_PATH_IMAGE064
,
Figure 139450DEST_PATH_IMAGE076
In the circular projection of cut handing over be parallel to arbitrarily XoyOn the plane of coordinate plane, obtain cutting and hand over circle to gather
Figure DEST_PATH_IMAGE208
,
Figure DEST_PATH_IMAGE210
On projection plane, calculate 1 donut, satisfy interior circle and the set of donut
Figure 39273DEST_PATH_IMAGE208
In 2 cut to hand over circle circumscribed, the cylindrical of donut and set
Figure 605383DEST_PATH_IMAGE210
In 2 cut to hand over the circle inscribes, the line at two point of contacts that the line at two point of contacts that the interior circle of donut is corresponding is corresponding with the cylindrical of donut has and intersects; According to concentrically ringed central coordinate of circle,
Figure 110314DEST_PATH_IMAGE014
Calculate
Figure 736467DEST_PATH_IMAGE040
,
Figure 858007DEST_PATH_IMAGE038
Jump to step 2;
Step 6: the quantity of judging low value contact point in the set of low value contact point be 2 and high value contact point set in the quantity of high value contact point be 2;
If high value contact point is 2 not all with the quantity of high value contact point, jump to step 8;
If high value contact point is 2 with the quantity of high value contact point, then the coordinate conversion that high value contact point and low value contact point are carried out makes cylinder axis
Figure 227809DEST_PATH_IMAGE080
Direction vector
Figure 977459DEST_PATH_IMAGE082
With zAxle is parallel; High value contact point and low value contact point are carried out ascending ordering by its z axial coordinate, make
Figure 774514DEST_PATH_IMAGE084
,
Figure 383349DEST_PATH_IMAGE086
zAxial coordinate increases progressively, and makes ,
Figure 301944DEST_PATH_IMAGE090
zAxial coordinate increases progressively, and then the sense of rotation vector of containment region is Or
Figure 834873DEST_PATH_IMAGE094
The rotation variation of containment region is set
Figure 546478DEST_PATH_IMAGE078
Initial value;
Step 7: calculate Around Or
Figure 727426DEST_PATH_IMAGE098
Rotation
Figure 242721DEST_PATH_IMAGE078
Vector after the angle With
Figure 6595DEST_PATH_IMAGE102
,
Figure 811740DEST_PATH_IMAGE104
Be the vertex of a cone, with
Figure 865146DEST_PATH_IMAGE100
For the axis direction vector, with Make auxiliary circular cone for semi-cone angle, wherein high value contact point is made the circumscribed cone of containment region, and the low value contact point is made the inscribe circular cone of containment region; Mistake respectively simultaneously ,
Figure 337082DEST_PATH_IMAGE108
Work obtains cutting the friendship circle perpendicular to the plane of axis with auxiliary conical intersection; Will
Figure 928600DEST_PATH_IMAGE102
,
Figure 888466DEST_PATH_IMAGE110
,
Figure 540027DEST_PATH_IMAGE112
,
Figure 319764DEST_PATH_IMAGE104
Shadow is on any a certain plane perpendicular to axis
Figure 183815DEST_PATH_IMAGE114
On, obtain respectively , ,
Figure 87683DEST_PATH_IMAGE120
,
Figure 880059DEST_PATH_IMAGE122
, will cut and hand over circular projection on the plane On; Can set up the binary nonlinear system of equations by following relation,
Figure 542301DEST_PATH_IMAGE124
Wherein
Figure 765472DEST_PATH_IMAGE126
,
Figure 768063DEST_PATH_IMAGE128
Be respectively
Figure 291449DEST_PATH_IMAGE130
, Corresponding cross section radius of circle,
Figure 290814DEST_PATH_IMAGE134
After change
Figure 831517DEST_PATH_IMAGE136
On the plane
Figure 209409DEST_PATH_IMAGE114
Projection; By finding the solution Nonlinear System of Equations, can calculate
Figure 278996DEST_PATH_IMAGE134
Coordinate; According to , ,
Figure 912606DEST_PATH_IMAGE128
,
Figure 684253DEST_PATH_IMAGE014
With
Figure 634891DEST_PATH_IMAGE100
, obtain the change vertex of a cone coordinate of the inside and outside female surface of containment region afterwards
Figure 517396DEST_PATH_IMAGE138
,
Figure 338722DEST_PATH_IMAGE140
According to the method for step 2, calculate the distance of low value contact point female surface outside containment region , calculate the high distance that is worth contact point female surface outside containment region
Figure 719205DEST_PATH_IMAGE144
And then according to the method for step 2, calculate the distance of all noncontact measuring points female surface outside containment region successively
Figure 405401DEST_PATH_IMAGE028
If And
Figure 319316DEST_PATH_IMAGE148
, then represent the variation deficiency, the anglec of rotation Become
Figure 937696DEST_PATH_IMAGE150
If
Figure 264773DEST_PATH_IMAGE152
Or
Figure 283544DEST_PATH_IMAGE154
, change excessively, there is measuring point to exceed containment region, the anglec of rotation
Figure 289546DEST_PATH_IMAGE078
Become
Figure 317545DEST_PATH_IMAGE156
Judge
Figure 499128DEST_PATH_IMAGE078
Whether the difference of the iterative value that front and back are 2 times is less than the error permissible value of setting
Figure 954380DEST_PATH_IMAGE018
If
Figure 57465DEST_PATH_IMAGE078
The difference of the iterative value that front and back are 2 times is less than the error permissible value
Figure 623576DEST_PATH_IMAGE018
, illustrate and find the 5th contact point, then will
Figure 925244DEST_PATH_IMAGE100
,
Figure 551397DEST_PATH_IMAGE138
,
Figure 266413DEST_PATH_IMAGE140
Assignment is given respectively ,
Figure 792389DEST_PATH_IMAGE056
,
Figure 58285DEST_PATH_IMAGE158
, and jump to step 2; Otherwise, the then operation of repeating step 7;
Step 8: judge whether high value contact equals 5 with low value contact point quantity sum;
If high value contact is not equal to 5 with low value contact point quantity sum; Jump to step 10; Otherwise, carry out dimensional variations, the dimensional variations amount is set
Figure 667121DEST_PATH_IMAGE160
Initial value;
Step 9: establish high value contact point coordinate, low value contact point coordinate is
Figure 575034DEST_PATH_IMAGE162
,
Figure 585715DEST_PATH_IMAGE164
, then each low value contact point all satisfies following formula,
Figure 553671DEST_PATH_IMAGE166
Each low value contact point all satisfies following formula,
Figure 243279DEST_PATH_IMAGE168
More than in two formulas
Figure 954883DEST_PATH_IMAGE170
,
Figure 820071DEST_PATH_IMAGE172
Figure 958928DEST_PATH_IMAGE174
,
Figure 119968DEST_PATH_IMAGE178
With
Figure 149421DEST_PATH_IMAGE182
,
Figure 688987DEST_PATH_IMAGE184
,
Figure 742393DEST_PATH_IMAGE186
,
Figure 582173DEST_PATH_IMAGE188
,
Figure 62833DEST_PATH_IMAGE190
Be unknown quantity, can set up five yuan of Nonlinear System of Equations like this; According to the method for step 7, judged whether that the noncontact point exceeds containment region; If there is measuring point to exceed the error containment region, then will
Figure 620853DEST_PATH_IMAGE192
Assignment is given
Figure 805847DEST_PATH_IMAGE160
If there is not measuring point to exceed containment region, then will Assignment is given
Figure 417274DEST_PATH_IMAGE160
Judge
Figure 197011DEST_PATH_IMAGE160
Whether the difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 61062DEST_PATH_IMAGE018
If
Figure 875434DEST_PATH_IMAGE160
The difference of the iterative value that front and back are twice is less than the error permissible value of setting
Figure 697897DEST_PATH_IMAGE018
, illustrate and find the 6th contact point, jump to step 10; Otherwise, carry out dimensional variations again, the operation of repeating step 9;
Step 10: judge that whether high value contact and low value contact point quantity sum are more than or equal to 6;
If high value contact and low value contact point contact point quantity sum are more than or equal to 6, with in the contact point set 5 be 1 combination, be calculating object with 5 contact points in 1 combination wherein, determine the dimensional variations amount according to the mode that the exploratory trace in the step 8,9 is adjusted Size; If
Figure 163830DEST_PATH_IMAGE160
Less than the error permissible value of setting
Figure 426184DEST_PATH_IMAGE018
, judge whether to satisfy criterion, jump to step 11 if satisfy criterion, do not change 1 combination if do not satisfy criterion, recomputate , judge that again iteration is gone down successively; If
Figure 173878DEST_PATH_IMAGE160
Greater than the error permissible value of setting
Figure 910889DEST_PATH_IMAGE018
, jump to step 2;
If high value contact and low value contact point contact point quantity sum then jump to step 2 less than 6;
Step 11: the vertex of a cone coordinate, axis direction vector, cone angle and the conicity that provide the Minimum Area circular cone.
CN201310255464.2A 2013-06-25 2013-06-25 A kind of computing method of the part conicity based on Minimum Area Active CN103292771B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201310255464.2A CN103292771B (en) 2013-06-25 2013-06-25 A kind of computing method of the part conicity based on Minimum Area

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201310255464.2A CN103292771B (en) 2013-06-25 2013-06-25 A kind of computing method of the part conicity based on Minimum Area

Publications (2)

Publication Number Publication Date
CN103292771A true CN103292771A (en) 2013-09-11
CN103292771B CN103292771B (en) 2015-12-02

Family

ID=49094033

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201310255464.2A Active CN103292771B (en) 2013-06-25 2013-06-25 A kind of computing method of the part conicity based on Minimum Area

Country Status (1)

Country Link
CN (1) CN103292771B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110657775A (en) * 2019-10-17 2020-01-07 上海佩尼医疗科技发展有限公司 Method for measuring conicity by three-coordinate scanning method

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4196523A (en) * 1977-02-07 1980-04-08 Mitsubishi Jukogyo Kabushiki Kaisha Method of centering hollow cylindrical workpiece
CN101010644A (en) * 2004-09-03 2007-08-01 日矿金属株式会社 Methods for determining and machining worked surface of plate-like material and apparatus for these methods
JP2010117260A (en) * 2008-11-13 2010-05-27 Epson Toyocom Corp Correction parameter preparation method of attitude detector, device for correction parameter preparation of attitude detector, and attitude detector
CN102162728A (en) * 2010-12-17 2011-08-24 南京工程学院 Method for evaluating minimum area of line profile error of cross section of skirt part of variable-ellipse piston

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4196523A (en) * 1977-02-07 1980-04-08 Mitsubishi Jukogyo Kabushiki Kaisha Method of centering hollow cylindrical workpiece
CN101010644A (en) * 2004-09-03 2007-08-01 日矿金属株式会社 Methods for determining and machining worked surface of plate-like material and apparatus for these methods
JP2010117260A (en) * 2008-11-13 2010-05-27 Epson Toyocom Corp Correction parameter preparation method of attitude detector, device for correction parameter preparation of attitude detector, and attitude detector
CN102162728A (en) * 2010-12-17 2011-08-24 南京工程学院 Method for evaluating minimum area of line profile error of cross section of skirt part of variable-ellipse piston

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
黄美发 等: "表面形貌评定方法对比分析", 《机械设计》, vol. 29, no. 5, 31 May 2012 (2012-05-31), pages 1 - 4 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110657775A (en) * 2019-10-17 2020-01-07 上海佩尼医疗科技发展有限公司 Method for measuring conicity by three-coordinate scanning method

Also Published As

Publication number Publication date
CN103292771B (en) 2015-12-02

Similar Documents

Publication Publication Date Title
CN103278126B (en) A kind of sphericity error assessment method for part based on Minimum Area
CN102865862B (en) Measurement method of non-horizontalization free established station
CN108871256B (en) Roundness error evaluation algorithm
CN103486984B (en) The detection method of profile right alignment in a kind of wind-tunnel
CN103292773B (en) A kind of symmetry error evaluation method based on Minimum Area
CN103256916A (en) Evaluation method of part flatness error based on minimum area
CN107990856B (en) Spatial position error detection method for over-range workpiece
CN102944204A (en) Method for detecting cross-section profile by utilizing two-dimensional measuring machine
CN107330142A (en) A kind of measuring point method arrow evaluation method of On-machine Test based on STL models
CN103759672A (en) Vision measurement method for ice cream stick plane contour dimensions
CN103223628B (en) A kind of method of on-line checkingi gear wheel profile error
CN106643643A (en) Non-contact target coordinate measuring method
CN103294920B (en) A kind of part Cylindricity error evaluation based on Minimum Area
CN102997875A (en) Method for analyzing uncertainty in high-precision measurement of complex spiral curved surfaces
CN104483891A (en) Method for improving machine tool space movement precision
CN103471572A (en) Total station networking measurement method of large-scale structural component
CN103292769B (en) A kind of plane inclination error detection method based on Minimum Area
WO2021128614A1 (en) Method for measuring and evaluating error of feature line-based arc cam profile
CN106091958A (en) The method measuring circular arc works radius based on arc height chord length method
CN104215185A (en) Method for calibrating central position of transformer by virtue of light-pen type portable three-coordinate measurement system
CN103292771A (en) Method for calculating part conicity based on minimum zone
CN108332642A (en) A kind of right-angle head accuracy checking method
CN105627918A (en) Axle hole reference on-site and quick leading out tool and method for visual precision measuring
CN103292770B (en) A kind of method calculating function size of cone part
CN103310106B (en) The computing method of a kind of hole in piece part system acts

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C41 Transfer of patent application or patent right or utility model
CB03 Change of inventor or designer information

Inventor after: Chen Leilei

Inventor after: Zhong Yanru

Inventor after: Sun Yonghou

Inventor after: Zhang Kuikui

Inventor after: Huang Meifa

Inventor after: Gong Wenfeng

Inventor after: Peng Zhiguo

Inventor before: Chen Leilei

Inventor before: Zhong Yanru

Inventor before: Sun Yonghou

Inventor before: Huang Meifa

Inventor before: Kuang Bing

COR Change of bibliographic data
TA01 Transfer of patent application right

Effective date of registration: 20151029

Address after: 541004 East District School of mechanical and electrical engineering, Guilin University of Electronic Technology, 1 Jinji Road, Qixing District, Guilin, the Guangxi Zhuang Autonomous Region

Applicant after: Guilin University of Electronic Technology

Address before: 541004 graduate school, Guilin University of Electronic Technology, 1 Jinji Road, Qixing District, Guilin, the Guangxi Zhuang Autonomous Region

Applicant before: Chen Leilei

C14 Grant of patent or utility model
GR01 Patent grant